Question

suppose $5,000 is invested in an account at an annual interest rate of 2.7% compounded continuously. how long (to the nearest tenth of a year) will it take the investment to double in size?

Answer 1

The basic equation for continuous compounding is as follows:
$A=Pe^{rt}$
Plugging in the given values gives:
$10000=5000e^{0.027t}$
Dividing both sides by 5000, we get:
$2=e^{0.027t}$
Take natural logs of each side:
$ln\ 2=0.027t$
from which we find that t = 25.67 years.